The Weight Calculation of a Carton of Soda Water: AnEngineering Approach

Have you ever wondered about the precise weight of a carton of soda water? This article delves into the calculation of the weight of a carton containing 12 bottles of soda water. We will explore the geometric shape of a soda bottle, the volume and mass calculations, and the total weight including the empty cardboard box.

Introduction to Soda Bottle Dimensions

A 1.25-liter bottle of soda water, also known as sparkling water, is a common household item. In this article, we will use a specific example of a bottle that is 285 millimeters high and has a diameter of 85 millimeters. We will then calculate the volume of a single bottle, the weight of soda water, and finally the total weight of a carton containing 12 bottles.

Volumes and Weights Involved

The first step in this calculation is to determine the volume of a single 1.25-liter (1250 milliliters) bottle of soda water. The volume of a cylinder is calculated using the formula:

V πr2h

where r is the radius of the bottle, which is half of the diameter.

Dimensions and Calculations

Given the diameter of the bottle is 85 millimeters, the radius is:

r 85 mm / 2 42.5 mm 0.0425 m

The height of the bottle is 285 millimeters, which is 0.285 meters. Plugging these values into the volume formula:

V π(0.0425)2 × 0.285

Using the value of π as approximately 3.14:

V 3.14 × (0.0425)2 × 0.285 ≈ 0.0059688269 m3

Weight of the Soda Water and Total Bottle Weight

Knowing that one milliliter of water weighs 1 gram (or 0.001 kilograms), the weight of the soda water in one bottle is:

1250 grams 1.25 kg

The weight of the empty bottle is 80 grams (0.080 kg). Therefore, the total weight of one bottle of soda water is:

1.25 kg 0.080 kg 1.33 kg

Carton Weight and Final Calculation

Now, we need to calculate the total weight of a carton containing 12 bottles. The weight of 12 bottles is:

12 × 1.33 kg 15.96 kg

The cardboard box weighs 750 grams, which is 0.75 kg. Therefore, the total weight of the carton with the soda water bottles and the cardboard box is:

15.96 kg 0.75 kg 16.71 kg

Thus, a carton of 12 bottles of soda water would weigh approximately 16.71 kilograms.

Dimensions of the Carton

Given the dimensions of the bottle, let's consider the dimensions of the carton that can hold 12 such bottles. If we assume the bottles are arranged in a 3x4 configuration within the carton, we can calculate the dimensions of the carton. Each bottle has a height of 285 millimeters and a diameter of 85 millimeters.

For a 3x4 arrangement:

Carton length 4 bottles × 85 mm 340 mm 0.34 m

Carton height 3 bottles × 285 mm 855 mm 0.855 m

Carton thickness 285 mm 0.285 m

These dimensions ensure a snug fit for the 12 bottles.

Volume of the Carton

The volume of the carton is calculated as:

V length × height × thickness 0.34 m × 0.855 m × 0.285 m 0.0853 m3

However, to simplify the weight calculation, we will assume a cuboid shape. The side length of the cuboid (a) can be found using the volume formula:

a3 0.0204 m3

Side length, a 0.02041/3 ≈ 0.2732 m

Thus, the dimensions of the cuboid carton are approximately:

Length 0.2732 m, Height 0.2732 m, Thickness 0.2732 m

Conclusion

Through this detailed calculation, we have determined that a 12-bottle carton of soda water, including the empty cardboard box, would weigh approximately 16.71 kg. This calculation is crucial in logistics and packaging design to ensure efficient handling and transportation of soda water.

Understanding the weight and dimensions of packaging is essential in various industries, such as retail and manufacturing. Stay tuned for more such articles on packaging and logistics calculations.